Stability diagrams of the periodic motions of a pendulum with an oscillating axis
The present paper deals with periodic rotations of a parametrically excited nonlinear oscillator, without taking the dissipation into account. The Cesari method is used to obtain the generating solutions, a number of periodic rotations of a single type are established and their stability is studied in the case when the values of two parameters are small. A number of solutions of practical interest are continued numerically into the domain of large values of the parameters. The bifurcation diagrams of periodic solutions are constructed, containing domains of their stability (to a first approximation) and the bifurcations of the appearance and change in the stability of these solutions are clarified.
parametrically excited nonlinear oscillator
scientific article; zbMATH DE number 4131725